Theorem hbmo1 1802

Description: Bound-variable hypothesis builder for "at most one."

Assertion

Ref	Expression
hbmo1	|- (E*xph -> A.xE*xph)

Proof of Theorem hbmo1

Step	Hyp	Ref	Expression
1		hbe1 1363	. . 3 |- (E.xph -> A.xE.xph)
2		hbeu1 1781	. . 3 |- (E!xph -> A.xE!xph)
3	1, 2	hbim 1354	. 2 |- ((E.xph -> E!xph) -> A.x(E.xph -> E!xph))
4		df-mo 1776	. 2 |- (E*xph <-> (E.xph -> E!xph))
5	4	albii 1346	. 2 |- (A.xE*xph <-> A.x(E.xph -> E!xph))
6	3, 4, 5	3imtr4i 236	1 |- (E*xph -> A.xE*xph)

Syntax hints:   -> wi 3  A.wal 1296  E.wex 1326  E!weu 1771  E*wmo 1772

This theorem is referenced by:  moanmo 1831  mopick2 1837  mopick2OLD 1838  moexex 1841  2eu3 1855  morex 15662

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7  ax-7 1304  ax-gen 1305  ax-4 1319  ax-5o 1321  ax-6o 1324

This theorem depends on definitions:  df-bi 164  df-an 242  df-ex 1327  df-eu 1775  df-mo 1776

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